1. Field of the Invention
The invention relates to the analysis and retrieval of signals. It is usable whenever it is desirable to accurately determine the evolution in time of a signal measured by sampling. It finds a particularly important although not exclusive, application in systems comprising a central measurement unit, provide for effecting filtering, sampling and analog/digital conversion operations, as well as multiplexing in the case of application of several signals, and a computer with terminals for the storage or retrieval of the data in digital (tables of the values of the signals at successive time t.sub.i) or graphic form.
2. Prior Art
When high analysis accuracy is required, at the present time a very high sampling rate is adopted so that the variations of the signal between two consecutive sampling times are small. The intermediate points may then be assessed with satisfactory accuracy by linear interpolation or by a low order polynomial function. In the case of retrieval in graphic form, this final interpolation is made by the retrieval apparatus itself which joins the samples together, by straight segments in the most frequent case, by segments of a circle or a sinusoid with high performing apparatus. This approach has the drawback of requiring the collection of a very large amount of data. It is considered that, for a signal having a band B (the band of the signal being defined as the frequency below which is contained 99% of the energy of the signal), the sampling frequency must be greater than 20B for the accuracy to be better than 10.sup.-2 in the case of a linear interpolation. The study of this type of interpolation shows that a good restoration of the signal, even using a polynomial interpolation of an order higher than 2, requires a high ratio, in practice greater than 5, between the sampling frequency and the band of the signal.
As soon as the passband B becomes high, which is the case for rapid transitory signals, the system must have a very high sampling rate, a very high digital transmission rate and, when the retrival is to take place with a time lag, a storage capacity in relation to the preceding rates. The overall cost of the system may consequently become very high.
It is further known (Shannon's theorem) that any point may be calculated between two consecutive samples of a signal with restricted spectrum, of band B, provided that the sampling frequency F.sub.e is greater than the Shannon frequency 2B. Unfortunately, the analytic expression of the signal x(t) as a function of the samples taken only converges very slowly and gives rise to very heavy calculations, which are difficult to apply in practice and practically exclude real time operation. On the other hand, the use of this expression allows, at least in theory, a sampling rate much slower than in the preceding case, very close to twice the band of the signal.
Still other systems have been proposed. They are used for example in certain digital oscilloscopes. They use a moderate sampling rate compared with the band of the signals. But they only allow restoration in the case of sinusoidal or, at all events, periodical signals.